Isotropic maps and moment map flow
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914758277464064 |
|---|---|
| author | Jauberteau, François Rollin, Yann |
| author_facet | Jauberteau, François Rollin, Yann |
| contents | We consider the moduli space of isotropic maps from a closed surface $Σ$ to a symplectic affine space and construct a Kähler moment map geometry, on a space of differential forms on $Σ$, such that the isotropic maps correspond to certain zeroes of the moment map. The moment map geometry induces a modified moment map flow, whose fixed point set correspond to isotropic maps. This construction can be adapted to the polyhedral setting. In particular, we prove that the polyhedral modified moment map flow induces a strong deformation retraction from the space of polyhedral maps onto the space of polyhedral isotropic maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11347 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isotropic maps and moment map flow Jauberteau, François Rollin, Yann Differential Geometry Symplectic Geometry 5299, 53D12 We consider the moduli space of isotropic maps from a closed surface $Σ$ to a symplectic affine space and construct a Kähler moment map geometry, on a space of differential forms on $Σ$, such that the isotropic maps correspond to certain zeroes of the moment map. The moment map geometry induces a modified moment map flow, whose fixed point set correspond to isotropic maps. This construction can be adapted to the polyhedral setting. In particular, we prove that the polyhedral modified moment map flow induces a strong deformation retraction from the space of polyhedral maps onto the space of polyhedral isotropic maps. |
| title | Isotropic maps and moment map flow |
| topic | Differential Geometry Symplectic Geometry 5299, 53D12 |
| url | https://arxiv.org/abs/2404.11347 |